The new variety originated as a result of a controlled cross between the strawberry plants ‘Marathon’ (U.S. Plant Pat. No. 12,817) and ‘Sonora’ (U.S. Plant Pat. No. 13,386) in an ongoing breeding program, and was discovered as a seedling in Monterey Country, Calif. in 1999. The original seedling of the new cultivar was asexually propagated by stolons in a Shasta County, Calif. Propagules were transplanted to a controlled breeding plot in Monterey Country, Calif., where the variety was identified and selected for further evaluation. ‘Driscoll Osceola’ was subsequently asexually propagated and underwent further testing in Hillsbourough County, Fla. for three years. This propagation and testing has demonstrated that the combination of traits disclosed herein which characterize the new variety are fixed and retained true to type through successive generations of asexual reproduction.